E.T. Copson. Metric Spaces. Cambridge Tracts in Mathematics 57, Cambridge University Press, 1992.  Home/Search   Document Not in Database   Summary   Related Articles

....Section 5.4 defines a complete ultra metric space based on time truncation. Time guardedness is defined in Section 5.5 and a semantics for time guarded specifications is provided in Section 5.6 5. 1 A resum e of metric spaces A more thorough treatment of metric spaces can be found in, for instance, [16]. Definition 18 (Metric space) For set A and d : A Theta A Gamma IR, the pair hA; di 20 is a metric space if for all x and y 2 A: 1) d(x; y) 0 (2) d(x; y) 0 , x = y (3) d(x; z) 6 d(x; y) d(y; z) for all z 2 A hA; di is called an ultra metric space if constraint (3) is replaced by ....

.... (e) e for all e 2 E n n, ffl f n;k ( n (f) k (f) for all k n 1 and f 2 F n , ffl l 0 k ( k (f) l 0 k (f n;k ( n (f) l 0 n ( n (f) for all k n 1 and f 2 F n , ffl A 0 k ( k (f) A 0 n ( n (f) for all k n 1 and f 2 F n , 8 From the theory of metric spaces [16] it is known that for any Cauchy sequence (E n ) there exists a subsequence (E i n ) with d(E i n ; E i k ) 6 1=2 n for all k n 1. Moreover, the limit of (E n ) if any) is identical to the limit of (E i n ) 29 ffl n (f) 0 n n (f 0 ) iff k (f) 0 k k (f 0 ) for all k n ....

E.T. Copson. Metric Spaces. Cambridge Tracts in Mathematics 57, Cambridge University Press, 1992.

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